Question

Solve the system of homogeneous equations:
x + y - 2z = 0
2x + y - 3z = 0
5x + 4y - 9z = 0

Answer 1

Answer:

x=z,y=z,z=z

Step-by-step explanation:

Cramer's Rule:

it says that

$x=\frac{\triangle}{\triangle_{1}}\\\\\\y=\frac{\triangle}{\triangle_{2}}\\\\\\z=\frac{\triangle}{\triangle_{3}}$

where Δ is determinant of matrix A,Δ1,Δ2,Δ3 are the determinant of A when column 1,2,3 are replaced by coefficient matrix respectively.

$\triangle=\left|\begin{array}{ccc}1&1&-2\\2&1&-3\\5&4&-9\end{array}\right|=0$

it cannot be solve by Cramer's rule and Inverse matrix method.

It can be solve in terms of other variable,by Gauss -Jordon Elimination.

As

$x=z,y=z,z=z$